Fixed that for you.
Nope.
COA is "Busoshoku".
Hardening is "Busoshoku Koka".
Hardening is more difficult than ordinary armament.
says who, Saint headcanon that they are fundamentally different?
kokaa is literally called hardening.. no one says it its harder some folks don't incorporate it in there fighting hence they don't have it? ... its clear as crystal that any fodder having coa can hardening their blade... so anyone with coa has the capability of doing so unless its not a part of their main arsenal aside from invisible arnament
both are called Coa.. sanji has deflected much vast attacks with just his leg in invisible arnament compared to Luffy's koka my man needs koka too often hues his invisible arnament ain't that fancy like sanjis.
some can even argue that no one has even pushed sanji to use koka..
your argument is a logical fallacy.. stemming from ignorance...that fodder in Dressrosa can do it but sanji can't (someone on a vastly different level in haki) .. and sanji hasn't shown it he doesn't have it? ... not taking into account most of the time he incorporates it into his DJ so logically if he intensifies his flames he'd be using more arnament..
so there is no "next level arnament" or "koka is harder" it's just some even having it not really needing it or never been pushed to use it..
Another point you're dismissing is.. if the animators literally give sanji hardening.. doesn't it prove it even further? coz oda will potentially never have sanji introduced to hardening because he already has it but doesn't use it as often or he's never required to.. oda would be dumb he'd do that